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This paper presents a workspace adaptive control method for the end-effector trajectory tracking of flexible robot arms in the presence of parametric uncertainties. A manifold is designed to describe the desirable behavior of the robot-system in terms of end-effector trajectory tracking and link vibration damping. A control scheme and the parameter update law are derived such that convergence of the motion of the robot to the designed manifold is guaranteed while the boundedness of parameter estimation is ensured. Stability of the system is verified by using the Lyapunov stability theory. Simulations were carried out to illustrate the effectiveness of the proposed adaptive control method.